Wednesday morning at the National Press Club in Washington, D.C., Green Party presidential candidate Jill Stein spoke to about a dozen people–and a couple dozen empty chairs. She had gone to the capital, in advance of the Green Party convention in Baltimore, to announce her running mate: Cheri Honkala. So who is Honkala? And for that matter, who is Stein? Here’s the first thing they’ll tell you: They’re candidates not named Barack Obama or Mitt Romney.

Born in the 1980s, the Green Party’s national profile peaked in 2000, when Ralph Nader took 2.7% of the popular vote in the chaotic presidential election that put George W. Bush in office. (One imagines Al Gore still wakes in the night cursing Nader’s name.) Not long after, in 2002, the Green Party recruited a physician and health advocate named Jill Stein to run for governor in Massachusetts. She lost that race and three more in the state over the next decade, while making two successful bids for Lexington Town Meeting representative. Meanwhile, the Green Party candidates in 2004 and 2008 failed to get more than 150,000 votes.

The election fight between Obama and Romney will be close, and a third-party candidate who mounts a significant campaign might be cause for concern as November nears–whether that’s libertarian Gary Johnson or the Green Party’s Stein. For now, Stein says she’s still introducing herself to the American people, trying to generate interest in the party that’s deflated over the past decade.

On Wednesday, Stein and Honkala, an anti-poverty advocate from Philadelphia, stood in front of a Green Party banner—an eagle swooping in front of a sunflower filled with stars—and laid out their “Green New Deal.” It’s a plan they say will lower unemployment while providing options for free higher education, downsizing the military, ending tax breaks and addressing climate change. Stein, with silver hair and a bright wardrobe, spoke in measured tones. She said that while Romney and Obama were quibbling about who outsourced more jobs and whether the Affordable Care Act levied a tax or a fee, she was offering “the green future that we deserve.”

The campaign is banking on support from college kids—a good constituency for politicians who want to forgive student debt—and activists involved in the Occupy Wall Street movement. When asked whether the campaign aligned with the Occupiers, Honkala said they were the “perfect” candidates for the group, and ready to capitalize on people’s distaste for the 1%. “I am a formerly homeless mother of two children. I have spent my entire life living at or below the federal poverty level,” Honkala said. “Every day for the last 25 years, I have worked with poor and homeless families.”

Stein and Honkala are trying to occupy a space left by voters, particularly left-leaners, who are fed up with Obama and uninterested in Romney. They expect to be an alternative option on the ballot in 40 states. And they said they bring a different kind of politics to the table, though it doesn’t appear to be a less divisive brand. When TIME asked where they shared common ground with the other candidates—despite their differences—neither had a response. Stein laughed, incredulous. Honkala said: “Do we?”

To point out that the Green Party ticket won’t win its bid for the White House is like saying that Stephen Colbert isn’t really as conservative as he pretends to be on his show: it’s obvious and misses the point. Third-partiers run to win new followers for their cause and—mostly—to have their ideas heard. Their highest electoral hope is to become an inconvenience for mainstream candidates. “You can win an election by winning the office,” Stein says, “but we can also win the day by driving the solutions, the real solutions.”

At best, that platitude probably means some of their ideas getting folded into the Democratic platform. The campaign has gone from all-volunteer to having 12 paid members of staff. If their application for matching federal election funds is approved–as they expect–that number may triple. It might not be much compared to the mainstream campaigns, but Stein and Honkala say the Green Party is primed to make the front-runners take notice.